yes you could have each ship if you wanted too, you can buy ships with energy credits. But your skills would mean that only one type would be very effective. Unless you are just a failure at spending skill points in which case every type would be equally ineffective.
thats lame. so since im tactical officer i have to be an escort to have good ship?
You could spec for the other ship types instead of you want to. But you cant spec for them all at the same time. Also there are some bonuses to sticking with the ship that matches your career type, but you dont have to.
You do not have enough skillpoints to spec everything though, so you will pick a ship type, weapon type, and improve the skills that improve the bridge officers you have chosen/customized. Different ship types have different skill needs
with that said skillpoints would come a bit slower once you used up all the leveling content. It probably would have been faster to make three characters to the level cap, one for each ship type, than just maxing one in the capless system.
But i would probably have tried to max myself out also if they had the old capless system, just to do it.